1. Field of the Invention
This invention relates generally to the field of automatic calibration of sensors in a closed loop transducer system. More particularly, the invention relates to the calibration for stray capacitances of a capacitive-sensing sensor in an electrostatic force-rebalancing accelerometer. Still more particularly, the invention relates to a sensor with top and bottom plates facing a centered mass supported by springs from a support frame and an electronic force-rebalancing system coupled to the sensor and to a method and apparatus for balancing mismatch in stray capacitance between the mass and the top and bottom plates.
2. Description of the Prior Art
FIGS. 1 and 2 illustrate a capacitive sensor shown generally at 10. FIG. 1 shows the sensor in a partially cut-away perspective view. FIG. 2 shows a plan view of the mass-spring-support frame assembly. The sensor includes a body including a top cover (or cap) 12, a bottom cover (or cap) 14, and a central (or seismic) mass 16 supported by springs 32, 34 from a generally rectangular frame 18 which receives the central mass 16 therein between cover plates 12 and 14. Sensor assembly 10 is preferably machined from wafers of a non-metallic monocrystalline material such as silicon, germanium, quartz, gallium arsenide, gallium phosphate, etc.
A spring support structure or connecting arrangement to support mass 16 from outer frame 18 is provided in a cavity between mass 16 and frame 18 and includes four top L-shaped spring members 32 and four bottom L-shaped springs 34. The preferred embodiment of the sensor 10 is described in U.S. Pat. No. 5,652,384 issued to I/O Sensors and in pending U.S. application Ser. No. 08/516,501 (assigned to I/O Sensors), both such patent and application incorporated by reference herein.
FIG. 3 is a cross section illustration of the sensor of FIGS. 1 and 2. When a force acts in a perpendicular direction to conductive surfaces 52, 52 of mass 16, top and bottom springs 32, 34 are deflected upwardly or downwardly relative to the illustration of FIG. 3. For a small deflection, springs 32, 34 are deformed linearly with input force applied perpendicularly to the top and bottom surfaces of mass 16. Such linear movement of the springs enables an extremely accurate measurement of a variable related to input force by measuring the displacement of mass 16 from the rest position. Such variable is preferably acceleration where forces are constant or dynamic of a frequency below the natural frequency of the sensor structure.
The sensor 10 of FIG. 3 is schematically shown in FIG. 4 to demonstrate and illustrate the operation of a capacitive sensor and electrostatic force feedback system for the measurement of acceleration. The sensor 10 is combined with analog and digital electronic circuits to sense the position of mass 16 between conductive plates 50 of top and bottom covers 12, 14. Electrostatic force feedback is provided by the feedback circuits to return mass 16 to an equilibrium position between plates 12.
The accelerometer system of FIG. 4 is placed in several states by a micro-computer based switch controller 100 which controls the opening and closing of various switches S.sub.1 -S.sub.13. The switch controller operates at a clock frequency of 128 KHz. A repetitive cycle which includes 32 states is produced by controller 100. FIG. 5 illustrates the opening and closing of switches S.sub.1 -S.sub.13 for each cycle. Each cycle starts with the end of the forcing period and begins with the first of several sensing phases. Each cycle includes three phases: Sensing Phase, Sample Phase, and Forcing Phase. A description of each state of the arrangement of FIG. 4 under control of switch controller 100 follows.
State 0: Sensing Phase: Voltage Equalization
During State 0 Switch S5 is opened thereby disconnecting the forcing voltage V.sub.F from center pin or lead 96 from the conductive regions 52 of mass 16. Very shortly thereafter, switch S9 is closed which rapidly discharges charge on the conductive regions 52 and brings them to ground or zero volts. The reference voltages +V.sub.R and -V.sub.R are applied to conductive regions 50 of the sensor top and bottom plates 12, 14 respectively, because switches S1 and S3 are closed.
State 1: Sensing Phase: Charge Summation
Next, Switch S9 opens and very shortly thereafter, switch S6 closes thereby connecting the sensor center pin 96 to the inverting input of operational amplifier (op amp) OA1. Because switches S7 and S8 are closed during this time, the inverting input of OA1 is forced to the offset voltage of the operational amplifier which is typically less than 100 micro volts (.mu.V) in absolute value.
State 2: Sensing Phase: Charge Transfer
Next switches S7 and S8 open, leaving only capacitor C.sub.1 in the feedback path of op amp OA1 in preparation for the charge transfer from the sensor 10. In addition, the charge injected from switch S7 onto capacitor C.sub.1 is balanced by the charge injected via switch S8 onto C.sub.2 thereby providing first order cancellation of the parasitic effect at the output of op amp OA1.
State 3: Sensing Phase: Sense Position of Mass 16 Between Top and Bottom Plates 50
Next, charge is transferred from the sensor 10 to the op amp OA1 by opening switches S1 and S3 and very shortly after closing switches S2 and S4. As a result, a voltage change of V.sub.R occurs on the sensor top conducting plate 50 and -V.sub.R on the bottom conducting plate 50 both with respect to the sensor center lead 96 which remains at the offset of the sense op amp OA1 plus the charge injection pedestal of S8-C.sub.2 after a short transient.
Therefore charge .DELTA.Q=Q.sub.1 +Q.sub.2 is transferred to the sensor center lead 96 where Q.sub.1 =V.sub.R C.sub.T and Q.sub.2 =-V.sub.R C.sub.B, where C.sub.T represents the capacitance between the top conducting plate 50 and the top of mass 16 plate 52, and C.sub.B represents the capacitance between the bottom plate 50 and the bottom of mass 16 plate 52. As a result, charge of amount .DELTA.Q=V.sub.R (C.sub.T -C.sub.B) is transferred onto the feedback capacitor C.sub.1.
At the end of state 3, the op amp OA1 output on lead 97 settles to the voltage value, ##EQU1## .epsilon..sub.0 =dielectric constant, A=area of conducting plates
d=distance between top and bottom plates 50, and PA0 x=distance that mass 16 has moved from the center position between top and bottom plates, ##EQU2##
As a result, the sense voltage on lead 97 can be approximated as a linear function of displacement x from a center position for .vertline.x.vertline.&lt;&lt;d, which applies under normal operating conditions.
State 4: Sample Phase
During state 4, the sample/hold circuit arrangement 99 including op amp OA2 and switches S10, S11, S12, S13 acquires the voltage ##EQU3## at its output 98 by going into the sample mode with S10 and S12 open and S11 and S13 closed. After settling for one state time, such switches change back into the hold mode by opening switches S10 and S12 and closing switches S11 and S13. Very shortly thereafter, the hold mode is entered during which forcing of mass 16 to its center position is performed.
States 5-31: Forcing Phase
In the forcing phase, voltage V.sub.F is applied to the sensor conductive areas 52 via lead 96. Simultaneously, the voltage +V.sub.R is applied to the top plate 50 and voltage -V.sub.R is applied to the bottom plate 50. The sense op amp OA1 is disconnected from the sensor 10 while the sample/hold circuit 99 holds at its output lead 98 the last sampled value of voltage representative of the sensor position. The cycle is repeated at the overall system sample rate.
The description of the operation of FIG. 4 assumes that there are no stray capacitances between the conductive plate 50 of top cover 12 and conductive region 52 of mass 16 which defines the "top" capacitance C.sub.T and between the conductive plate 50 of bottom cover 14 and bottom conductive region 52 of mass 16 which defines the "bottom" capacitance C.sub.B.
In actual fabrication of the sensor of FIG. 3, the top and bottom conductive regions 52, 52 of mass 16 may not be in precise registration with the top and bottom conductive regions 50 of top and bottom plates 12, 14. For example, the mass 16 may have a fixed tilt (that is, it is rotated about the mass center) with respect to the parallel top and bottom plates 12, 14. Or, the mass 16 might be level, but the top or bottom plate 12, 14 may tilt with respect to the proof mass 16. Or, either the top or bottom plate 12, 14 may be bowed up (concave up) or bowed down (concave down). In each case, the stray capacitance from the mass top surface 52 to the cover top surface 50 is different from the stray capacitance from the mass bottom surface 52 to the bottom cover surface 50. It can be shown that the system of FIG. 4 has its signal to noise ratio degraded due to stray capacitance mismatch.